The Otherwoods
Roughly 1,000 movies are produced in India every year. Of these, around 200 films are produced by Bollywood each year. Of course, few people outside of India are aware of this, and many foreigners assume that all of Indian cinema is Bollywood. Contrary to popular opinion, "Bollywood" only refers to Hindi films. So where do the other 800 movies come from?
Kollywood and Tollywood
The Tamil film industry is called "Kollywood". Whenever an actor/actress/singer/composer wants to make it big in any Indian film industry, they start here. Many iconic Hindi stars, from Aishwariya Rai to Kajol, debuted in Kollywood. Tollywood (the Telugu film industry) produces more films per year than Hindi cinema, even though it is much less famous. Outside of Hindi Cinema, these two industries are the largest and most popular in India, and they share a lot: tropes, actors, composers, directors. Both are located in Southeastern India, and the majority of their audience is located in the same area. Indians who are unfamiliar with these industries often lump them together as 'Tamil' or 'South Indian' and associate them with political regionalism.
Indeed, whenever South India in general is brought up by North Indians among themselves they will, almost as a Verbal Tic, then say "inna RRRRRAScaleh" (an exaggerated Tamil pronunciation of "rascal", referring to the line often famously used by South Indian superstar Rajnikanth).
These two film industries are today thought of as the Large Ham of Indian films, even by Bollywood standards. The films are unabashedly escapist. The heroes are always unapologetic Stus of the highest order. The Love Interest (called a "heroine", even if she never does anything heroic) is usually a straight-up chick and Damsel in Distress. The action will be over the top and the subtitles will be difficult to understand. Every film will have copious amounts of comic relief as most films attempt to stuff in as much action, romance, and comedy as possible. This all-in-one genre combination is called 'masala'. Even movies with a serious subject matter (politics, horror, history, mythology) more or less follow the same pattern. Also, they are all musicals. All of them. Combine all of that with the low quality special effects and you get an industry of Narmy, So Bad It's Good movies. There are exceptions, such as I Have Found It, a Kollywood adaptation of Sense and Sensibility, which combines slice-of-life drama, and romance with some mild satire of the South Indian film industries, but these exceptions are relatively few and far between.
What the mainstream of Kollywood and Tollywood have going for them is that they tend to be more action-oriented than Bollywood and more on the "gritty" side. Where Bollywood is lots of romance with token action, South Indian movies are lots of action with Token Romance. Where Bollywood movies tend to focus on the wealthy, these movies are more likely to feature middle-class and working-class characters (partly because of political influences in the past). Also, they are usually very high-energy. The main reason that the stuey Action Hero is accepted is because the actors are required to be entertaining and enthusiastic enough to pull off such overbearing roles. There are also pretty high standards set for music and choreography; the two most famous Indian composers and the most famous dancer/choreographer are actually from Kollywood. Both industries are more experimental than Bollywood: they hire more new talent and are more likely to try new techniques in cinematography and special effects. The Tamil film Endhiran, for instance included robot designs from Stan Winston's studio.
It might be easier for tropers to think of it this way: If Bollywood is like a Bishonen Hero, then Kollywood is his snarky Anti-Hero Lancer and Tollywood is the Hot-Blooded Big Guy.
These film industries are also noteworthy for producing lots of politicians, à la Schwarzenegger. The two biggest examples are M.G. Ramachandran (of Kollywood, often shortened to 'MGR') and N.T. Rama Rao (of Tollywood, shortened to 'NTR'). Both formed their own political parties and spun fanatical film Fandoms into huge voting blocs. Both also pandered to the poor (especially MGR, who was portrayed as a fighter on their behalf in the movies) and to regional pride. Another example is former actress Vijayashanti, who started out portraying stock love interests in Tollywood, bucked the boys-only club by graduating to cop heroine roles in the nineties, and later went onto a political career. She is the inspiration for a minor character in I Have Found It.
Mollywood
If Kollywood is The Lancer in this lineup and Tollywood is the Big Guy, then Mollywood is the Smart Guy.
"Mollywood" refers to the Malayalee industry, from the Southwest Indian state of Kerala. Historically, these films tended to be a little more thoughtful, subversive, and low-key than their southeastern counterparts, but Mollywood also churns out its share of cheap action films, intended to compete for eyeballs with Malayalee dubs of the Tollywood and Kollywood mainstays. The Mollywood action films tend to unimpressive compared to the Tollywood and Kollywood output: they have much smaller budgets, not much action choreography, and usually star middle-aged men who originally made their reputations in more cerebral films, and aren't really action hero material.
Another minor quirk of Mollywood cinema is that Kerala has a relatively high percentage of Christians, and a very long history of hosting them (with one group claiming to have been evangelized by St. Thomas The Apostle). As a result of this, Mollywood portrayals of Christians tend to be less caricatured and more naturalistic than Bollywood's portrayals of Christians.
Not to be confused with the Mormon film industry, or LDS Cinema, also known as Mollywood.